Tools

"... The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed -calculus with dependent types. Syntax is treated in a style similar to, but more general than, Martin-Lof's system of ariti ..."

The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed -calculus with dependent types. Syntax is treated in a style similar to, but more general than, Martin-Lof&apos;s system of arities. The treatment of rules and proofs focuses on his notion of a judgement. Logics are represented in LF via a new principle, the judgements as types principle, whereby each judgement is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higher-order judgements and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logic-independent tools such as proof editors and proof checkers can be constructed.

"... this paper we reconsider the foundations of modal logic, following MartinL of's methodology of distinguishing judgments from propositions [ML85]. We give constructive meaning explanations for necessity (2) and possibility (3). This exercise yields a simple and uniform system of natural deductio ..."

this paper we reconsider the foundations of modal logic, following MartinL of&apos;s methodology of distinguishing judgments from propositions [ML85]. We give constructive meaning explanations for necessity (2) and possibility (3). This exercise yields a simple and uniform system of natural deduction for intuitionistic modal logic which does not exhibit anomalies found in other proposals. We also give a new presentation of lax logic [FM97] and find that it is already contained in modal logic, using the decomposition of the lax modality fl A as

"... Grammatical Framework (GF) is a special-purpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for lineariz ..."

Grammatical Framework (GF) is a special-purpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for linearizing syntax trees and parsing strings. GF can describe both formal and natural languages. The key notion of this description is a grammatical object, which is not just a string, but a record that contains all information on inflection and inherent grammatical features such as number and gender in natural languages, or precedence in formal languages. Grammatical objects have a type system, which helps to eliminate run-time errors in language processing. In the same way as an LF, GF uses...

"... As more resources are added to computer networks, and as more vendors look to the World Wide Web as a viable marketplace, the importance of being able to restrict access and to insure some kind of acceptable behavior even in the presence of malicious adversaries becomes paramount. Many researchers h ..."

As more resources are added to computer networks, and as more vendors look to the World Wide Web as a viable marketplace, the importance of being able to restrict access and to insure some kind of acceptable behavior even in the presence of malicious adversaries becomes paramount. Many researchers have proposed the use of security protocols to provide these security guarantees. In this paper, we develop a method of verifying these protocols using a special purpose model checker which executes an exhaustive state space search of a protocol model. Our tool also includes a natural deduction style derivation engine which models the capabilities of the adversary trying to attack the protocol. Because our models are necessarily abstractions, we cannot prove a protocol correct. However, our tool is extremely useful as a debugger. We have used our tool to analyze 14 different authentication protocols, and have found the previously reported attacks for them. Keywords Model checking, security ...

by
James Mckinna, Robert Pollack
- Journal of Automated Reasoning, 1999

"... Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention ..."

Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention redex positions or residuals. Then we outline the meta theory of Pure Type Systems, leading to the strengthening lemma. One novelty is our use of named variables for the formalization. Along the way we point out what we feel has been learned about general issues of formalizing mathematics, emphasizing the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts.

The specifications of most of the nowadays ubiquitous informations systems include integrity constraints, i.e. conditions rejecting so-called &quot;invalid&quot; or &quot;inconsistent &quot; data. Information system consistency and query answering have been formalized referring to classical logic implicitly assuming that query answering only makes sense with consistent information systems. In practice, however, inconsistent as well as consistent information systems need to be queried. In this paper, it is first argued that classical logic is inappropriate for a formalization of information systems because of its global notion of inconsistency. It is claimed that information systems inconsistency should be understood as a local notion. Then, it is shown that minimal logic, a constructivistic weakening of classical logic which precludes refutation proofs, provides for local inconsistencies that conveniently reflect a practitioner&apos;s intuition. Further, minimal logic is shown to be a convenient foundation fo...

Computer algebra systems (CASs) and automated theorem provers (ATPs) exhibit complementary abilities. CASs focus on efficiently solving domain-specific problems. ATPs are designed to allow for the formalization and solution of wide classes of problems within some logical framework. Integrating CASs and ATPs allows for the solution of problems of a higher complexity than those confronted by each class alone. However, most experiments conducted so far followed an ad-hoc approach, resulting in tailored solutions to specific problems. A structured and principled approach is necessary to allow for the sound integration of systems in a modular way. The Open Mechanized Reasoning Systems (OMRS) framework was introduced for the specification and implementation of mechanized reasoning systems, e.g. ATPs. The approach was recasted to the domain of computer algebra systems. In this paper, we introduce a generalization of OMRS, named OMSCS (Open Mechanized Symbolic Computation Systems). We show how OMSCS can be used to soundly express CASs, ATPs, and their integration, by formalizing a combination between the Isabelle prover and the Maple algebra system. We show how the integrated system solves a problem which could not be tackled by each single system alone.